It was a game which manager Craig Levein had predicted as he saw his team struggle against a side who clearly lifted their game for their SPL opponents.
The Tangerines began with enthusiasm, coming close in the third minute when Willo Flood fired in a free-kick to Tony Bullock's right-hand corner which the ex-United keeper did well to turn around the post.
But the swirling wind did nothing to help entertainment as the game degenerated into a long-ball affair, with neither team making any headway into their opponents' box.
There had been little to excite the fans until the 39th minute when some neat exchanges within the Tangerine ranks ended with Flood cutting in from the left flank and curling an inviting ball, which the on-rushing Noel Hunt just failed to connect with at the near post.
As the visitors toiled, Sean Dillon chipped for Hunt to volley with venom just narrowly wide from 20 yards as half-time approached.
After the break and playing with the wind, United upped the ante and really should have taken the lead before on-loan striker Jordan Robertson was pulled to the ground by Andy Dowie for a penalty in the 65th minute.
Robertson, only signed this week from Sheffield United, had threatened and was clearly fouled giving the referee an easy decision. His strike partner Nel Hunt stepped up to send Bullock the wrong way.
However it was not game over as County shocked their SPL hosts in the 77th minute when a deep free-kick was knocked back into goal for the unmarked Andy Barrowman to chest into the net from four yards.
Robertson responded with venom, volleying against the underside of the bar two minutes later.
But the youngster was rewarded for his efforts with a well-taken goal a couple of minutes from time.
A superb four-man move involving Christian Kalvenes, Morgaro Gomis, Mark Kerr and Robertson ended with the youngster stroking the ball home from six yards after Kalvenes had crossed from the left.